# Ram has 18 coins in the denominations of Rs 1, Rs 2 and Rs 5 . If their total value is Rs 54 and the number of Rs 2 coins are just greater than that of Rs 5 coins., then find the number of Rs 1 coins in his hand

Dear Student,

Given : Ram has 18 coins in the denominations of Rs 1, Rs 2 and Rs 5  ,

Let , Total number of Rs. 1 coins  =  ,

Total number of Rs. 2 coins  =  ,

Total number of Rs. 5 coins  =  , So We get

x  + y  + z  = 18                                                                  --- ( 1 )

Also given : their total value is Rs 54  , So

( 1 ) x + ( 2 ) y + ( 5 ) z =  54

x + 2 y + 5 z =  54                                                             --- ( 2 )

Also given : Number of Rs 2 coins are just greater than that of Rs 5 coins. So

y > z

Now we can use hit and trial method to satisfy these condition . ( As we have three variables and two equations )

At y = 4 , We get from equation 1 : x + 4 + z  =  18

x + z  =  14                                                                 --- ( i )

And we get from equation 2 : x + 2 ( 4 ) + 5 z  =  54

x + 5 z  =  46                                                             --- ( ii )

Now ( ii ) - ( i ) we get

4 z= 32 ,  = 8   But here We get y =  4 and z  = 8  , So y $\ngtr$ z ( As per third condition number of Rs 2 coins are just greater than that of Rs 5 coins )

So, That is not our solution .

Now , At y = 8 , We get from equation 1 : x + 8 + z  =  18

x + z  =  10                                                                 --- ( a )

And we get from equation 2 : x + 2 ( 8 ) + 5 z  =  54

x + 5 z  =  38                                                             --- ( b )

Now ( b ) - ( a ) we get

4 z= 28 ,  = 7   But here We get y =  8 and z  = 7  , So y > z  , Then substitute value of y and z in equation 1 and get

x  + 8 + 7 = 18

x =  3

Therefore,

Total number of Rs . 1 coins in Ram's hand  =  3                                                   ( Ans )